TY - JOUR
T1 - Data fusion via intrinsic dynamic variables
T2 - An application of data-driven Koopman spectral analysis
AU - Williams, Matthew O.
AU - Rowley, Clarence Worth
AU - Mezić, Igor
AU - Kevrekidis, Yannis
N1 - Publisher Copyright:
© CopyrightEPLA, 2015.
PY - 2015/2/1
Y1 - 2015/2/1
N2 - We demonstrate that the Koopman eigenfunctions and eigenvalues define a set of intrinsic coordinates, which serve as a natural framework for fusing measurements obtained from heterogeneous collections of sensors in systems governed by nonlinear evolution laws. These measurements can be nonlinear, but must, in principle, be rich enough to allow the state to be reconstructed. We approximate the associated Koopman operator using extended dynamic mode decomposition, so the method only requires time series of data for each set of measurements, and a single set of "joint" measurements, which are known to correspond to the same underlying state. We apply this procedure to the FitzHugh-Nagumo PDE, and fuse measurements taken at a single point with principal-component measurements.
AB - We demonstrate that the Koopman eigenfunctions and eigenvalues define a set of intrinsic coordinates, which serve as a natural framework for fusing measurements obtained from heterogeneous collections of sensors in systems governed by nonlinear evolution laws. These measurements can be nonlinear, but must, in principle, be rich enough to allow the state to be reconstructed. We approximate the associated Koopman operator using extended dynamic mode decomposition, so the method only requires time series of data for each set of measurements, and a single set of "joint" measurements, which are known to correspond to the same underlying state. We apply this procedure to the FitzHugh-Nagumo PDE, and fuse measurements taken at a single point with principal-component measurements.
UR - http://www.scopus.com/inward/record.url?scp=84924873555&partnerID=8YFLogxK
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U2 - 10.1209/0295-5075/109/40007
DO - 10.1209/0295-5075/109/40007
M3 - Article
AN - SCOPUS:84924873555
SN - 0295-5075
VL - 109
JO - EPL
JF - EPL
IS - 4
M1 - 40007
ER -